Which album is this song from? Algorithm is baffled by Rammstein

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k-Nearest Neighbour (k-NN) classification algorithm has been applied to the dataset in order to classify the songs into albums using computational methods. If the predictions are accurate, we can infer that albums significantly differ from each other, which would further aid my Mutter/Sehnsucht vs Rosenrot debate.

Unfortunately, k-NN performs poorly on Rammstein’s discography. The best obtained score is 5/11 songs correctly classified, that is for Herzeleid. Precision and recall scores, summarized below, indicate an abundance of both false negatives and false positives. For instance, for RAMMSTEIN album, both precision and recall are 0.

Low recall means that songs from a particular album are not categorized into the same album by the algorithm. Low precision means that the algorithm also thinks that a lot of songs from other albums belong to an album in question. The only acceptable scores are for Herzeleid, although recall is still quite poor.

Album (Precision, Recall):
- Herzeleid (0.7142857, 0.4545455)
- LIEBE IST FÜR ALLE DA (0.2500000, 0.1875000)
- Mutter (0.1428571, 0.1818182)
- RAMMSTEIN (0.0000000, 0.0000000)
- Reise, Reise (0.2000000, 0.1818182)
- ROSENROT (0.2307692, 0.2727273)
- Sehnsucht (0.2500000; 0.2727273)

Choosing top predictors (loudness, c12, c04) and features used for previous analyses (danceability, energy, valence, loudness and tempo) did not majorly improve things.

Training a classifier using so many categories (Audio Features, timbre components), whilst having a small corpus (82 songs) will most probably lead to poor performance, as the variability is extremely high. No definite conclusions can be drawn from k-NN results.

Hierarchical k-Means clustering: Sehnsucht & Mutter are Neighbours, Rosenrot is their Distant Friend

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K-NN is a supervised learning algorithm that is useful for classification and regression problems. As was seen from the previous tab, the performance is lacking.

I have decided to use an unsupervised learning algorithm made to tackle clustering problems, that is hierarchical k-means.

To begin with, I wanted to know whether it is sensible to conduct these analyses at all. I generated a distance matrix to see if there are any preliminary clustering trends. I decided to focus on the features that were determined to be potentially characteristic after analyzing the density plots in previous tabs. The distance matrix on the left based on danceability, energy, valence, loudness and tempo shows the Euclidean distance between album pairs. The closer to 0 (black colour), the less distance, thus the more similar are albums. There is a black diagonal line that indicates that albums are identical, that is distance = 0, because we are comparing an album to itself.

The matrix shows that Rosenrot seems to be similar to RAMMSTEIN, whereas Sehnsucht is quite different from every other album. Looks promising!

The results of the hierarchical k-means can be seen in the second plot. The algorithm grouped similar objects together. Objects within each cluster are more similar to each other than to those outside the cluster.

The amount of clusters (3) was chosen after applying the elbow method. In this method, sum of squares at each number of clusters (in my case, from 2 to 5) are calculated and plotted. Afterwards, by determining the “elbow” (a point at which the slope changes from steep to shallow), the user can determine an optimal number of clusters. This method is not as precise as other, more mathematically-rigorous cluster validation methods, but seemed to work for the current (small) dataset.

Indeed, as can be seen from both the distance matrix and hierarchical k-means clustering, Sehnsucht and Mutter share more similarities with each other than with Rosenrot, which is grouped with RAMMSTEIN, which supports the idea that Rosenrot is somehow different from Mutter and Sehnsucht.

Valence and Energy in context: Rammstein is angry, but also happy and not calm at all

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Spotify’s Audio Features sometimes might seem a bit isolated from the real world. Valence is said to be “a measure describing the musical positiveness conveyed by a track”. The higher the valence score, the more positive, happy and cheerful the song sounds. Energy is labelled as “perceptual measure of intensity and activity”. Tracks with high energy are typically fast, loud and noisy.

But how perceptually sound these measures really are?

To tackle this question, I decided to look at the corpus in the context of valence-arousal model of emotion (circumplex model). In this model, emotions are distributed in a 2D circular space. The dimensions are arousal (Spotify’s energy) and valence. The combinations of these features result in 4 emotion quadrants - calm, happy, sad or angry. Placing Rammstein’s songs in this model can provide us with an overview of the emotions that their music evokes.

The results of the classification are quite fascinating. Firstly, Rammstein has no calm songs, as the quadrant is absolutely empty. This is not unexpected, as Rammstein has only few ballads and those are in the calm category. The songs that are the closest to being calm are Los and Laichzeit. Perceptually, these two tracks might sound more monotone compared to others in happy, which places them lower on the energy scale, but they are still loud and fast. It is also a bizarre and grim experience seeing a song about incest and bestiality (Laichzeit) in the happy category…

Secondly, the happiest songs are Bestrafe mich and Eifersucht. Please take a listen and judge yourself whether these songs sound happy! I would guess that they do not. To me, Ausländer is the happiest track out of the whole discography, but it is in the angry quadrant. These misalignments might indicate that Spotify’s features do not directly correspond to arousal and valence of the circumplex model.

The angriest song is Rammlied, which I agree with. This powerful album opening song has an apocalyptic vibe to it, with pronounced guitar riffs and devilish Till’s vocals juxtaposed with church choir in the background. This is a grandstanding song that just sounds powerful and furious.

Unsurprisingly, Ein Lied is the most unhappy song. Ein Lied is one of their slowest songs, with acoustic guitars, ethereal synthesizers and theremin-like keyboards being the focus of the song’s instrumental. The percussion is completely absent from this song. The vocal line is soft, partly spoken, partly sung using low breathy tones, which is atypical of Rammstein.

Overall, the majority of songs are in the angry category and none in calm, which, in my opinion, aligns with the public’s perception of Rammstein and metal music in general. No specific trends per album can be seen.

Rammstein’s preferred tempo: does it align with Moelants’?

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Moelants (2002) showed that there is a certain preferred tempo at around 125 BPM. This natural tempo corresponds with both repeated motor actions, such as finger tapping, and perceived tempo in musical data. As can be seen from the plot, Rammstein’s songs mostly fall in 115-140 BPM frame, with a visible peak at 120-130 BPM.

Moelants’ findings, current corpus’ tempo distribution and Spotify’s own value distribution for tempo align pretty neatly, with noticeable spikes at 120-130 BPM marks.

Although metal music can cover a wide scale of tempos, preferred tempo range is still reflected in Rammstein’s discography, further indicating that it indeed might be more natural to compose songs in that tempo range.

Tempograms: Ich will is faster than Feuer frei!?

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The two cyclic tempograms at the left illustrate Spotify’s estimated tempo for two typical songs: Feuer Frei! and Ich will. Overall, the estimated tempo (yellow line) is strong and stable throughout the duration of both songs. The excerpts where the line breaks correspond to fragraments of the songs where minimal instrumental accompaniment is present.

Interestingly, Feuer Frei! sounds way faster to me than Ich will. I would even say that Feuer Frei! is one of the fastest songs in the corpus, whereas Spotify claims that it is actually on the slower side. My personal estimation of tempo for Feuer Frei! would stand at around twice Spotify’s - 190 BPM. Ich will’s BPM makes sense, as it is indeed ~128 BPM.

Because Spotify’s BPM estimation might be based on tatums, which are subdivisions of beats, we get this inaccurate tempo. In short, if there is one particular tempo, Spotify probably captures twice and thrice the BPM. Spotify most probably chose the lower band, which we now see on the Feuer frei! tempogram - 95 BPM, whereas the true tempo is twice as fast - 190 BPM.

Here we saw an example of Spotify API’s faulty judgement, along with an accurate one. Spotify’s beat tracking technique is not bulletproof!

Popularity: Sehnsucht and Mutter are still relevant, but is Rosenrot?

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To take as much as I can from Spotify’s available data, I also explored the popularity metric. Spotify is a bit secretive about the algorithm behind popularity scores, so it is helpful to illustrate datapoints.

Spotify provides popularity scores on 3 levels: track, album and artist. All 3 levels can be seen on the interactive plot on the left. Feel free to explore and see where your favorite songs land!

Spotify’s documentation page tells us that “the value is between 0 and 100, with 100 being the most popular. The track popularity is calculated by algorithm and is based, in the most part, on the total number of plays the track has had and how recent those plays are. Artist and album popularity is derived mathematically from track popularity.”

In theory, if Rosenrot is the least favoured album, the popularity score on all levels should be the lowest among the discography. Conversely, Mutter and Sehnsucht should have the highest ratings. So does Spotify’s data actually support this hypothesis?

The answer is yes and also no. On the track level, Rosenrot does not contain only unpopular songs. On the album level, however, Rosenrot is the second least popular album (68), with Herzeleid occupying the first place. One can argue that the recency factor came into play here. Herzeleid (1995) was the band’s debut album, which came out 25 years ago. Rosenrot (2005) is relatively new. I think it is a bit tricky to compare such old albums to newer ones; still, Herzeleid’s median is higher (54) than Rosenrot’s (50). Moreover, album-level popularity differs by only 1 point.

As for Mutter (2001) and Sehnsucht (1997), although both of the albums were released a while ago, they are still very popular on both track and album levels. On the album level, Mutter (75) and Sehnsucht (74) share the second and the third place, respectively, overtaken only by RAMMSTEIN. RAMMSTEIN’s popularity might be explained by the fact that it is their most recent album (2019).

If we take a look at the track level, Mutter’s median is 60, the same value as RAMMSTEIN’s. Although Sehnsucht’s median is lower, it contains some of the most popular songs in the corpus - Du Hast (72) and Engel (68). Sonne (69), the highest rated song from Mutter is also in the top 5 most popular Rammstein’s songs at the moment.

What is going on with Liebe ist für alle da (2009), though? The tracks are low on the popularity scale, but the album’s popularity is comparatively high (70). These ratings seem counterintuitive. The explanation might be hidden in some Spotify’s algorithm’s pecularity, as the raw popularity is probably scaled separetely per level (track, album, artist).

The most attentive readers might have noticed, that atypical songs - Ein Lied (45, Rosenrot, 2005) and Roter Sand - Orchester Version (31, LIFAD, 2009) are not only the least popular songs from the albums, but also in the whole discography.

All in all, we can see a trend: despite being older albums, Sehnsucht (1997) and Mutter (2001) are more popular than their newer counterpart Rosenrot (2005).

“Constants” in the Corpus FIX

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(tbu)

(A)Typical Rammstein: perception and computation

Song	Mode	Key	Tempo	Loudness
Du Hast	Minor	A	125.11	-6.283
Ich will	Major	D	128.12	-4.254
Feuer Frei!	Major	Eb	95.14	-3.974
Hallomann	Major	Bb	172.00	-5.936
Te Quiero Puta!	Major	F	159.93	-5.305
Ausländer	Major	C	125.03	-4.159
Ein Lied	Major	F	122.32	-19.239
Roter Sand - Orchester Version	Major	G	82.42	-10.255

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For detailed, low-level audio analysis, typical and atypical songs have to be established.
What songs would make you exclaim “yes, of course this is Rammstein!”? Personally, I chose Du hast and Ich will. Of course, this approach is highly subjective and influenced by a plethora of external reasons, such as track popularity, familiarity with the artist, individual biases and tastes. To expand the notion of “typical” to include not only my personal judgements, but also those of a potentially impartial algorithm, standardizes z-scores based on all audio features were computed. The songs that scored nearest to 0, mainly Feuer Frei! and Hallomann were chosen as representatives.

The same approach was taken when selecting atypical songs. In my opinion, Te Quiero Puta! may be the most un-Rammstein song they have ever released. In the context of all their other recordings, this metal-meets-mariachi song sounds novel. Another unique track is Ausländer. It sounds so catchy and pop-y, that it might have been a successful (rock)club song. Unsurprisingly, z-scores (z > 2) indicated that Ein Lied and Roter Sand – Orchester Version differ from the rest of the corpus, as these are Rammstein’s ballads.

Summary:
- typical songs - Feuer Frei!, Hallomann, Ich will, Du Hast;
- atypical songs – Ein Lied, Roter Sand – Orchester Version, Te Quiero Puta!, Ausländer.

The Spotify Audio Features per song are presented in an interactive heat table on the left. Additionally, I compiled a playlist of typical/atypical songs! ↓ ADD PLAYLIST!!!!!!!!!!!!!!!!!!!!

FIX

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1st picture: chordogram for Te Quiero Puta!, 2nd picture: Ausländer (TBU: add titles directly to plots). Althought both of these songs are labeled as atypical by me, they are very different when compared by chordograms. For Te Quiero Puta!, D:maj is noted by a darker band throughout the song. Around 160, a yellow line, indicating a bridge has started. Ausländer chordogram, on the other hand, shows no clear patterns, except for darker bands at F:7 and D:maj.

FIX

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1st picture: SSM for Ausländer, 2nd picture: SSM for Du hast (TBU: add titles directly to plots). The self-similarity matrix for Ausländer shows very clear repetitiveness in both chroma and timbre plots. The checkerboard pattern shows that a passage is repeated throughout the song. In Du hast timbre plot, we can see a couple of thin (60, 170) yellow lines, which highlight novel parts, whereas in Ausländer, the yellow lines are thicker and re-occur throughout the song.

🔥 🤘 Why Rammstein? Get to know RQs and corpus 🤘 🔥